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Article Dans Une Revue Cambridge Journal of Mathematics Année : 2021

On the analogy between real reductive groups and Cartan motion groups. I: The Mackey-Higson bijection

Résumé

George Mackey suggested in 1975 that there should be analogies between the irreducible unitary representations of a noncompact reductive Lie group $G$ and those of its Cartan motion group $G_0$ − the semidirect product of a maximal compact subgroup of G and a vector space. He conjectured the existence of a natural one-to-one correspondence between "most" irreducible (tempered) representations of G and "most" irreducible (unitary) representations of $G_0$. We here describe a simple and natural bijection between the tempered duals of both groups, and an extension to a one-to-one correspondence between the admissible duals.
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Dates et versions

hal-01214358 , version 1 (12-10-2015)
hal-01214358 , version 2 (29-06-2021)

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Alexandre Afgoustidis. On the analogy between real reductive groups and Cartan motion groups. I: The Mackey-Higson bijection. Cambridge Journal of Mathematics, 2021, 9 (3), pp.551-575. ⟨10.4310/CJM.2021.v9.n3.a1⟩. ⟨hal-01214358v2⟩
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